The problem states that in the figure, $B$ is between $A$ and $C$, and $C$ is between $B$ and $D$. Given the following lengths:

• $AC = 10$
• $BD = 9$
• $BC = 7$

We are tasked with finding $AD$.

Solution:

1. Start by noting that $AC = AB + BC$. Since $B$ is between $A$ and $C$, we can find $AB$ by subtracting: $AB = AC - BC = 10 - 7 = 3$

2. Next, $AD$ is the total distance from $A$ to $D$, which can be broken down as $AD = AB + BD$. Substituting the values: $AD = AB + BD = 3 + 9 = 12$

Thus, the length of $AD$ is $\boxed{12}$.

Let me know if you'd like further details!

Here are some related questions:

1. How would the calculation change if $B$ was not between $A$ and $C$?
2. What if $AC$ and $BD$ were given as variables instead of specific numbers?
3. How can this concept be extended to three-dimensional geometry?
4. What if $C$ were not between $B$ and $D$, how would that affect $AD$?
5. How can you represent this problem using algebraic expressions?

Tip: Always check the relationships between the points (e.g., which point is between others) carefully before solving such geometry problems.